The sum of two numbers is $71$, and their difference is $9$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 71}$ ${x-y = 9}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 80 $ $ x = \dfrac{80}{2} $ ${x = 40}$ Now that you know ${x = 40}$ , plug it back into $ {x+y = 71}$ to find $y$ ${(40)}{ + y = 71}$ ${y = 31}$ You can also plug ${x = 40}$ into $ {x-y = 9}$ and get the same answer for $y$ ${(40)}{ - y = 9}$ ${y = 31}$ Therefore, the larger number is $40$, and the smaller number is $31$.